Lesson 4: Practice Problems

Problem 1

Find the exact length of each line segment.
Estimate the length of each line segment to the nearest tenth of a unit. Explain your reasoning.

Problem 2

Plot each number on the $x$ -axis: $\sqrt{16}, \sqrt{35}, \sqrt{66}$ . Consider using the grid to help.

Problem 3

Use the fact that $\sqrt{7}$ is a solution to the equation $x^{2} = 7$ to find a decimal approximation of $\sqrt{7}$ whose square is between 6.9 and 7.1.

Problem 4

Explain how you know that $\sqrt{37}$ is a little more than $6$ .
Explain how you know that $\sqrt{95}$ is a little less than $10$ .
Explain how you know that $\sqrt{30}$ is between $5$ and $6$ .

Problem 5

Plot each number on the number line: $6, \sqrt{83}, \sqrt{40}, \sqrt{64}, 7.5$

A number line with 6 evenly spaced tick marks and the integers 5 through 10 are indicated.

Problem 6

The equation $x^{2} = 25$ has two solutions. This is because both $5 \cdot 5 = 25$ , and also $- 5 \cdot - 5 = 25$ . So, 5 is a solution, and also -5 is a solution.

Select all the equations that have a solution of -4:

$10 + x = 6$
$10 - x = 6$
$- 3 x = - 12$
$- 3 x = 12$
$8 = x^{2}$
$x^{2} = 16$

Problem 7

Find all the solutions to each equation.

$x^{2} = 81$
$x^{2} = 100$
$\sqrt{x} = 12$

Problem 8 From Unit 5 Lesson 4

The points $(12, 23)$ and $(14, 45)$ lie on a line. What is the slope of the line?